President Barack Obama’s administration is quietly offering a quasi-amnesty for hundreds of thousands of illegal immigrants, while aiming to win reelection by mobilizing a wave of new Hispanic voters, say supporters of stronger immigration law enforcement.

The new rules were quietly announced Friday with a new memo from top officials at the US Immigration and Customs Enforcement (ICE) agency.

The “prosecutorial discretion” memo says officials need not enforce immigration laws if illegal immigrants are enrolled in an education center or if their relatives have volunteered for the US military. “They’re pushing the [immigration] agents to be even more lax, to...